Fall 2010

The KU Combinatorics Seminar meets on **Wednesdays,
3:00--4:00 PM in Snow 408.**
Please contact Jeremy Martin
if you are interested in speaking.

**Wednesday 8/25**

No seminar

**Wednesday 9/1**

Jeremy Martin

*Parking functions, embroidered permutations, and the Shi arrangement*

**Wednesday 9/8**

Jeremy Martin

*Parking functions, embroidered permutations, and the Shi arrangement II*

**Wednesday 9/15**

Brandon Humpert

**Ph.D. Oral Comprehensive Examination**

**Wednesday 9/22**

Josephine Yu (Georgia Tech)

*Linear Systems on Tropical Curves*__Abstract:__A tropical curve is a metric graph with possibly unbounded edges, and tropical rational functions are continuous piecewise linear functions with integer slopes. We define the complete linear system |D| of a divisor D on a tropical curve analogously to the classical counterpart. We investigate the structure of |D| as a cell complex and show that linear systems are tropical modules, finitely generated by vertices of the cell complex. Using a finite set of generators, |D| defines a map from the tropical curve to a tropical projective space, and the image can be extended to a parameterized tropical curve of degree equal to deg(D). The tropical convex hull of the image realizes the linear system |D| as an embedded polyhedral complex. We also show that curves for which the canonical divisor is not very ample are hyperelliptic. This is joint work with Christian Haase and Gregg Musiker.

**Wednesday 9/29**

Branden Stone

*Janet Bases*

**Wednesday 10/6**

No seminar

**Wednesday 10/13**

No seminar - Fall Break

**Friday 10/15, 4-5 PM, Snow 306**(note unusual time and place)

Drew Armstrong (University of Miami)

*The Ish Arrangement of Hyperplanes*__Abstract:__The Shi arrangement of hyperplanes plays an important role in the representation theory of affine Weyl groups. Its definition in type A is Shi(n)={x_i-x_j=0,1 : 1 ≤ i < j ≤ n}. This arrangement divides**R**^n into (n+1)^{n-1} regions --- an interesting number, yes? --- and it has beautiful combinatorics. In this talk I will introduce a new arrangement, called the Ish arrangement. You will like this arrangement. (Some of this is joint work with Brendon Rhoades.)

**Wednesday 10/20**

No seminar

**Wednesday 10/27**

William Espenschied

*Lower Bounds for Cubical Pseudomanifolds*

**Wednesday 11/3**

*Special double feature!*

Jay Schweig:*Borel ideals via Borel generators*

Jeremy Martin:*Updown numbers and the initial monomials of the slope variety*

**Wednesday 11/10**

William Espenschied

*Lower Bounds for Cubical Pseudomanifolds, II*

**Wednesday 11/17**

TBA

**Wednesday 11/24**

No seminar - Thanksgiving

**Wednesday 12/1**

Alex Schaefer

*Nontransitive Dice*

**Wednesday 12/8**

TBA

**Wednesday 12/15**

TBA

Jeremy Martin's home page

Last updated Mon 1/31/11